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Remarks on Littlewood–Paley Analysis

Published online by Cambridge University Press:  20 November 2018

Kwok-Pun Ho
Kwok-Pun Ho*
Affiliation:
Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong, China e-mail:[email protected]
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Abstract

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Littlewood–Paley analysis is generalized in this article. We show that the compactness of the Fourier support imposed on the analyzing function can be removed. We also prove that the Littlewood–Paley decomposition of tempered distributions converges under a topology stronger than the weak-star topology, namely, the inductive limit topology. Finally, we construct a multiparameter Littlewood–Paley analysis and obtain the corresponding “renormalization” for the convergence of this multiparameter Littlewood–Paley analysis.

Keywords

42B25Littlewood–Paley analysisdistributions
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 60 , Issue 6 , 01 December 2008 , pp. 1283 - 1305
Copyright
Copyright © Canadian Mathematical Society 2008

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